A homochiral tartrate-bridged dinuclear chromium(III) complex anion with a resonance-assisted hydrogen bond for proton conduction

The synthesis of a homochiral building block based on L-tartrate-chromium(III) complex anions is reported. The dinuclear complex anion, which contains two bridging L-tartrate ligands and one aromatic N-donor ligand coordinated to chromium(III) ions, exhibits a boat conformation in which intramolecular resonance-assisted hydrogen bonding is present. The sodium L-tartrate-chromium(III) compound with the formula Na[Cr2(bpy)2(L-tart)2H]·9H2O (1) crystallizes from a methanol-water solution as a high water content material in the monoclinic space group P2. The as-synthesized compound is only stable at high relative humidity and undergoes structural transformations during drying, which are accompanied by water loss. However, these transformations are reversible and upon wetting, the material returns to its high water content structure. Based on a combination of experimental techniques (PXRD, in situ ATR-FTIR and EPR spectroscopy), the structure of the complex anions appears to be insensitive to the humidity variable processes (wetting and drying). Due to the presence of several hydrogen acceptor and donor groups in the L-tartrate-chromium(III) complex anion, we investigated the proton transport properties of a sodium L-tartrate-chromium(III) compound by impedance spectroscopy under dry and wet conditions at different temperatures. Since the relative humidity affects the structural transformations in this system, it also has a large influence on the proton conductivity, which varies by up to four orders of magnitude depending on the degree of hydration. These results confirm that the proton conductivity can be tuned in flexible structures in which non-covalent interactions determine the crystal packing.

Unveiling the Quantitative Relationships between Electron Distribution and Steric Hindrance of Organic Amines and Their Reaction Rates with Carbonyl Sulfur: A Theoretical Calculation Investigation

The removal of carbonyl sulfide (COS) commonly contained in natural gas is of great significance but still very challenging via a widely employed absorption process due to its low reactivity and solubility in various commercial solvents. Artificial intelligence (AI) is playing an increasingly important role in the exploration of desulfurization solvents. However, practically feasible AI models still lack a thorough understanding of the reaction mechanisms. Machine learning (ML) models established on chemical mechanisms exhibit enhanced chemical interpretability and prediction performance. In this study, we constructed a series of solvent molecules with varying functional groups, including linear aliphatic amines, cyclic aliphatic amines, and aromatic amines and proposed a three-step reaction pathway to dissect the effects of charge and steric hindrance of different substituents on their reaction rates with COS. Chemical descriptors, based on electrostatic potential (ESP), average local ionization energy (ALIE) theory, Hirshfeld charges, and Fukui functions, were used to correlate and predict the electrophilic reactivity of amine groups with COS. Substituents influence the reaction rate by changing the attraction interaction of amine groups to COS molecules and the electron rearrangement in the electrophilic reaction. Furthermore, they have more pronounced steric effects on the reaction rate in the linear amines. The descriptors N_ALIE and q(N) were found to be crucial in predicting the reactivity of amine groups with COS. Present study provides a comprehensive understanding of the reaction mechanisms of COS with amine compounds, offers specific chemical principles for the development of chemistry-driven ML models, sheds light on other types of electrophilic reactions occurring on amine and phosphine groups, and guides the development of chemical solvents in gas absorption processes.

Enhancing hydrogen positions in X-ray structures of transition metal hydride complexes with dynamic quantum crystallography

Hirshfeld atom refinement (HAR) is a method which enables the user to obtain more accurate positions of hydrogen atoms bonded to light chemical elements using X-ray data. When data quality permits, this method can be extended to hydrogen-bonded transition metals (TMs), as in hydride complexes. However, addressing hydrogen thermal motions with HAR, particularly in TM hydrides, presents a challenge. At the same time, proper description of thermal vibrations can be vital for determining hydrogen positions correctly. In this study, we employ tools such as SHADE3 and Normal Mode Refinement (NoMoRe) to estimate anisotropic displacement parameters (ADPs) for hydrogen atoms during HAR and IAM refinements performed for seven structures of TM (Fe, Ni, Cr, Nb, Rh and Os) and metalloid (Sb) hydride complexes for which both the neutron and the X-ray structures have been determined. A direct comparison between neutron and HAR/SHADE3/NoMoRe ADPs reveals that the similarity between neutron hydrogen ADPs and those estimated with NoMoRe or SHADE3 is significantly higher than when hydrogen ADPs are refined with HAR. Regarding TM-H bond lengths, traditional HAR exhibits a slight advantage over the other methods. However, combining NoMoRe/SHADE3 with HAR results in a minor decrease in agreement with neutron TM-H bond lengths. For the Cr complex, for which high-resolution X-ray data were collected, an investigation of resolution-related effects was possible.

Hirshfeld Atom Refinement of Metal-Organic Complexes: Treatment of Hydrogen Atoms Bonded to Transition Metals

Hydrogen positions in hydrides play a key role in hydrogen storage materials and high-temperature superconductors. Our recently published study of five crystal structures of transition-metal-bound hydride complexes showed that using aspherical atomic scattering factors for Hirshfeld atom refinement (HAR) resulted in a systematic elongation of metal-hydrogen bonds compared to using spherical scattering factors with the Independent Atom Model (IAM). Even though only standard-resolution X-ray data was used, for the highest-quality data, we obtained excellent agreement between the X-ray and the neutron-derived bond lengths. We present an extended version of this study including 10 crystal structures of metal-organic complexes containing hydrogen atoms bonded to transition-metal atoms for which both X-ray and neutron data are available. The neutron structures were used as a benchmark, and the X-ray structures were refined by applying Hirshfeld atom refinement using various basis sets and DFT functionals in order to investigate the influence of the technical aspects on the length of metal-hydrogen bonds. The result of including relativistic effects in the Hamiltonian and using a cluster of multipoles simulating interactions with a crystal environment during wave function calculations was examined. The effect of the data quality on the final result was also evaluated. The study confirms that a high quality of experimental data is the key factor allowing us to obtain significant improvement in transition metal (TM)-hydrogen bond lengths from HAR in comparison with the IAM. Individual adjustments and better choices of the basis set can improve hydrogen positions. Average differences between TM-H bond lengths obtained with various DFT functionals upon including relativistic effects or between double-ζ and triple-ζ basis sets were not statistically significant. However, if all bonds formed by H atoms were considered, significant differences caused by different refinement strategies were observed. Finally, we examined the refinement of atomic thermal motions. Anisotropic refinement of hydrogen thermal motions with HAR was feasible only in some cases, and isotropically refined hydrogen thermal motions were in similar agreement with neutron values whether obtained with HAR or with the IAM.

How do density functionals affect the Hirshfeld atom refinement?

In this work, the effect of mixing different amounts of Hartree-Fock (HF) exchange with hybrid density functionals applied to the Hirshfeld atom refinement (HAR) of urea and oxalic acid dihydrate is explored. Together, the influence of using different basis sets, methods (including MP2 and HF) and cluster sizes (to model bulk effects) is studied. The results show that changing the amount of HF exchange, no matter the level of theory, has an impact almost exclusively on the H atom refinement parameters. Contrary to pure quantum mechanical calculations where good geometries are obtained with intermediate HF exchange mixtures, in the HAR the best match with neutron diffraction reference values is not necessarily found for these admixtures. While the non-hydrogen covalent bond lengths are insensitive to the combination of method or basis set employed, the X-H bond lengths always increase proportionally to the HF exchange for the analysed systems. This outcome is opposite to what is normally observed from geometry optimisations, i.e., shorter bonds are obtained with greater HF exchange. Additionally, the thermal ellipsoids tend to shrink with larger HF exchange, especially for the H atoms involved in strong hydrogen bonding. Thus, it may be the case that the development of density functionals or basis sets suitable for quantum crystallography should take a different path than those fitted for quantum chemistry calculations.

Influence of modelling disorder on Hirshfeld atom refinement results of an organo-gold(I) compound

Details of the validation of disorder modelling with Hirshfeld atom refinement (HAR) for a previously investigated organo-gold(I) compound are presented here. The impact of refining disorder on HAR results is discussed using an analysis of the differences of dynamic structure factors. These dynamic structure factor differences are calculated from thermally smeared quantum mechanical electron densities based on wavefunctions that include or exclude electron correlation and relativistic effects. When disorder is modelled, the electron densities stem from a weighted superposition of two (or more) different conformers. Here this is shown to impact the relative importance of electron correlation and relativistic effect estimates expressed by the structure factor magnitudes. The role of disorder modelling is also compared with the effect of the treatment of hydrogen anisotropic displacement parameter (ADP) values and atomic anharmonicity of the gold atom. The analysis of ADP values of gold and disordered carbon atoms showed that the effect of disorder significantly altered carbon ADP values and did not influence those of the gold atom.

Benzene and Borazine, so Different, yet so Similar: Insight from Experimental Charge Density Analysis

Although benzene and borazine are isoelectronic and isostructural, they have very different electronic structures, mainly due to the polar nature of the B-N bond. Herein, we present an experimental study of the charge density distribution obtained from the multipole model formalism and Hirshfeld atom refinement (HAR) based on high-resolution X-ray diffraction data of borazine B₃N₃H₆ (1) and B,B',B″-trichloroborazine (2) crystals. These data are compared to those obtained from HAR for benzene (4) and 1,3,5-trichlorobenzene (5) and further compared with values obtained from density functional theory calculations in the gas phase, where N,N',N″-trichloroborazine (3) was also included. The results confirm that, unlike benzene, borazines are only weakly aromatic with an island-like electronic delocalization within the B₃N₃ ring involving only the nitrogen atoms. Furthermore, delocalization indices and interacting quantum atom energy for bonded and non-bonded atoms were found to be highly suitable indicators capable of describing the origin of the discrepancies observed when the degree of aromaticity in 2 and 3 is evaluated using common aromaticity indices. Additionally, analysis of intermolecular interactions in the crystals brings further evidence of a weakly aromatic character of the borazines as it reveals surprising similarities between the crystal packing of borazine and benzene and also between B,B',B″-trichloroborazine and 1,3,5-trichlorobenzene.

Hirshfeld atom refinement based on projector augmented wave densities with periodic boundary conditions

Hirshfeld atom refinement (HAR) is an X-ray diffraction refinement method that, in numerous publications, has been shown to give H-atom bond lengths in close agreement with neutron diffraction derived values. Presented here is a first evaluation of an approach using densities derived from projector augmented wave (PAW) densities with three-dimensional periodic boundary conditions for HAR. The results show an improvement over refinements that neglect the crystal environment or treat it classically, while being on a par with non-periodic approximations for treating the solid-state environment quantum mechanically. A suite of functionals were evaluated for this purpose, showing that the SCAN and revSCAN functionals are most suited to these types of calculation.

A novel 2-(aminomethyl)pyridineH2PO4 crystal with second-order nonlinear optical performance

Single-crystal structure diagram and SHG response of (2-Ampy)H2PO4 crystal.

Vanishing of the atomic form factor derivatives in non-spherical structural refinement - a key approximation scrutinized in the case of Hirshfeld atom refinement

When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-spherical? The assumption that this particular term is very close to zero is generally made in non-spherical refinements (for example, implementations of Hirshfeld atom refinement or transferable aspherical atom models), unless the form factors are refinable parameters (for example multipole modelling). To evaluate this general approximation for one specific method, a numerical differentiation was implemented within the NoSpherA2 framework to calculate the derivatives of the structure factors in a Hirshfeld atom refinement directly as accurately as possible, thus bypassing the approximation altogether. Comparing wR₂ factors and atomic parameters, along with their uncertainties from the approximate and numerically differentiating refinements, it turns out that the impact of this approximation on the final crystallographic model is indeed negligible.

A quantum crystallographic approach to short hydrogen bonds

In this work we use high-resolution synchrotron X-ray diffraction for electron density mapping, in conjunction with ab initio modelling, to study short O-H⋯O and O+-H⋯O- hydrogen bonds whose behaviour is known to be tuneable by temperature. The short hydrogen bonds have donor-acceptor distances in the region of 2.45 Å and are formed in substituted urea and organic acid molecular complexes of N,N'-dimethylurea oxalic acid 2 : 1 (1), N,N-dimethylurea 2,4-dinitrobenzoate 1 : 1 (2) and N,N-dimethylurea 3,5-dinitrobenzoic acid 2 : 2 (3). From the combined analyses, these complexes are found to fall within the salt-cocrystal continuum and exhibit short hydrogen bonds that can be characterised as both strong and electrostatic (1, 3) or very strong with a significant covalent contribution (2). An additional charge assisted component is found to be important in distinguishing the relatively uncommon O-H⋯O pseudo-covalent interaction from a typical strong hydrogen bond. The electron density is found to be sensitive to the extent of static proton transfer, presenting it as a useful parameter in the study of the salt-cocrystal continuum. From complementary calculated hydrogen atom potentials, we attribute changes in proton position to the molecular environment. Calculated potentials also show zero barrier to proton migration, forming an 'energy slide' between the donor and acceptor atoms. The better fundamental understanding of the short hydrogen bond in the 'zone of fluctuation' presented in a salt-cocrystal continuum, enabled by studies like this, provide greater insight into their related properties and can have implications in the regulation of pharmaceutical materials.

A rare case of a 2:2:1 ternary cocrystal of pyridine sulfides and trithiocyanuric acid

We report a rare case of a 2:2:1 ternary cocrystal consisting of two trithiocyanuric acid molecules, two bis(pyridin-4-yl) sulfide molecules and 1,4-bis(pyridin-4-yl)tetrasulfane, namely, 1,3,5-triazinane-2,4,6-trithione-4-(pyridin-4-ylsulfanyl)pyridine-1,4-bis(pyridin-4-yl)tetrasulfane (2/2/1), 2C₃H₃N₃S₃·2C₁₀H₈N₂S·C₁₀H₈N₂S₄. This interesting crystal structure with five neutral molecules per asymmetric unit was synthesized and characterized by means of X-ray diffraction (XRD) experiments and quantum-chemical modelling. Among various specific interactions, hydrogen and halogen bridges have a significant role in stabilizing the crystal structure. In particular, the role played by stacking interactions has been revealed by structure analysis and theoretical calculations. Crystallization was spontaneous and reproducible. One of the components, 1,4-bis(pyridin-4-yl)tetrasulfane, has been characterized by XRD for the first time.

Further Validation of Quantum Crystallography Approaches

Quantum crystallography is a fast-developing multidisciplinary area of crystallography. In this work, we analyse the influence of different charge density models (i.e., the multipole model (MM), Hirshfeld atom refinement (HAR), and the transferable aspherical atom model (TAAM)), modelling of the thermal motion of hydrogen atoms (anisotropic, isotropic, and with the aid of SHADE or NoMoRe), and the type of radiation used (Mo Kα and Cu Kα) on the final results. To achieve this aim, we performed a series of refinements against X-ray diffraction data for three model compounds and compared their final structures, geometries, shapes of ADPs, and charge density distributions. Our results were also supported by theoretical calculations that enabled comparisons of the lattice energies of these structures. It appears that geometrical parameters are better described (closer to the neutron values) when HAR is used; however, bonds to H atoms more closely match neutron values after MM or TAAM refinement. Our analysis shows the superiority of the NoMoRe method in the description of H-atom ADPs. Moreover, the shapes of the ADPs of H atoms, as well as their electron density distributions, were better described with low-resolution Cu Kα data in comparison to low-resolution Mo Kα data.

The advanced treatment of hydrogen bonding in quantum crystallography

Although hydrogen bonding is one of the most important motifs in chemistry and biology, H-atom parameters are especially problematic to refine against X-ray diffraction data. New developments in quantum crystallography offer a remedy. This article reports how hydrogen bonds are treated in three different quantum-crystallographic methods: Hirshfeld atom refinement (HAR), HAR coupled to extremely localized molecular orbitals and X-ray wavefunction refinement. Three different compound classes that form strong intra- or intermolecular hydrogen bonds are used as test cases: hydrogen maleates, the tripeptide l-alanyl-glycyl-l-alanine co-crystallized with water, and xylitol. The differences in the quantum-mechanical electron densities underlying all the used methods are analysed, as well as how these differences impact on the refinement results.

Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K

The experimental electron density distribution (EDD) of 1-methyluracil (1-MUR) was obtained by single crystal X-ray diffraction (XRD) experiments at 23 K. Four different structural models fitting an extensive set of XRD data to a resolution of (sinθ/λ)max = 1.143 Å-1 are compared. Two of the models include anharmonic temperature factors, whose inclusion is supported by the Hamilton test at a 99.95% level of confidence. Positive Fourier residuals up to 0.5 eÅ-3 in magnitude were found close to the methyl group and in the region of hydrogen bonds. Residual density analysis (RDA) and molecular dynamics simulations in the solid-state demonstrate that these residuals can be likely attributed to unresolved disorder, possibly dynamical and long-range in nature. Atomic volumes and charges, molecular moments up to hexadecapoles, as well as maps of the molecular electrostatic potential were obtained from distributed multipole analysis of the EDD. The derived electrostatic properties neither depend on the details of the multipole model, nor are significantly affected by the explicit inclusion of anharmonicity in the least-squares model. The distribution of atomic charges in 1-MUR is not affected by the crystal environment in a significant way. The quality of experimental findings is discussed in light of in-crystal and gas-phase quantum simulations.

Actual Symmetry of Symmetric Molecular Adducts in the Gas Phase, Solution and in the Solid State

This review discusses molecular adducts, whose composition allows a symmetric structure. Such adducts are popular model systems, as they are useful for analyzing the effect of structure on the property selected for study since they allow one to reduce the number of parameters. The main objectives of this discussion are to evaluate the influence of the surroundings on the symmetry of these adducts, steric hindrances within the adducts, competition between different noncovalent interactions responsible for stabilizing the adducts, and experimental methods that can be used to study the symmetry at different time scales. This review considers the following central binding units: hydrogen (proton), halogen (anion), metal (cation), water (hydrogen peroxide).

Towards accurate and precise positions of hydrogen atoms bonded to heavy metal atoms

A comparison of five X-ray structures of transition-metal-bound hydride complexes, successfully refined using Hirshfeld Atom Refinement (HAR) against low resolution X-ray diffraction data (including the positions and ADPs of all hydrogen atoms), with neutron structures shows that using aspherical atomic scattering factors instead of spherical ones results in systematic elongation of metal-hydrogen bonds, which in the case of the highest-quality data leads to excellent agreement of the X-ray and the neutron-derived bond lengths.

Climbing Jacob's Ladder of Structural Refinement: Introduction of a Localized Molecular Orbital-Based Embedding for Accurate X-ray Determinations of Hydrogen Atom Positions

The positions of hydrogen atoms in molecules are fundamental in many aspects of chemistry. Nevertheless, most molecular structures are obtained from refinements of X-ray data exploiting the independent atom model (IAM), which uses spherical atomic densities and provides bond lengths involving hydrogen atoms that are too short compared to the neutron reference values. To overcome the IAM shortcomings, the wave function-based Hirshfeld atom refinement (HAR) method has been recently proposed, emerging as a promising strategy able to give element-hydrogen bond distances in excellent agreement with the neutron ones in terms of accuracy and precision. In this Letter, we propose a significant improvement of HAR based on the idea of describing the crystal environment explicitly in the underlying wave function calculation through a quantum mechanical embedding strategy that exploits extremely localized molecular orbitals. Test-bed refinements on a crystal structure characterized by strong intermolecular interactions are also discussed.